How to assign multi colors on a screw modifier
Materials are assigned at the face/polygon level. The screwed edges in your question have initially no materials. So I think you should extrude/scale down the initial half circle. Assign materials to the wanted parts and use the screw.

Something like that:



Though, geometry will be non manifold and this will be visible.

To correct that, you can use a mask modifier:

Do exactly as previously but do not scale down after extruding, just stay in place. Now with these newly selected vertices create a vertex group.

Color the faces, as before (even if faces are not visible).

Then add a mask modifier after the screw, using the created vertex group: